Transmission Fundamentals

Slides made by Yu-Chee Tseng

Electromagnetic Signal

� is a function of time

� can also be expressed as a function of

frequency

� Signal consists of components of different

frequencies

Time-Domain Concepts

� Analog signal - signal intensity varies in a smooth fashion over time

� No breaks or discontinuities in the signal

� Digital signal - signal intensity maintains a constant level for some period of time and then changes to another constant level

� Periodic signal - analog or digital signal pattern that repeats over time

s(t +T ) = s(t ) -∞< t < +∞

where T is the period of the signal

� Aperiodic signal - analog or digital signal pattern that doesn't repeat over time

Time-Domain Concepts (cont.)

� Peak amplitude (A)

� maximum value or strength of the signal over

time

� typically measured in volts.

� Frequency (f )

� Rate, in cycles per second, or Hertz (Hz), at

which the signal repeats.

Time-Domain Concepts (cont.)

� Period (T)

� amount of time it takes for one repetition of the signal

� T = 1/f

� Phase (φ) - measure of the relative position in time within a single period of a signal

� Wavelength (λ) - distance occupied by a single cycle of the signal

� Ex: Speed of light is v = 3x108 m/s. Then the wavelength is λf = v (or λ = vT).

Sine Wave Parameters

� General sine wave

� s(t ) = A sin(2πft + φ)

� note: 2π radians = 360° = 1 period

� Figure 2.3 shows the effect of varying each of the

three parameters

� (a) A = 1, f = 1 Hz, φ = 0; thus T = 1s

� (b) Reduced peak amplitude; A=0.5

� (c) Increased frequency; f = 2, thus T = ½

� (d) Phase shift; φ = π/4 radians (45 degrees)

Sine Wave Parameters

Frequency-Domain Concepts

� An electromagnetic signal can be made up

of many frequencies.

� Example: s(t) = (4/π) · (sin(2πft) +

(1/3)sin(2π(3f)t))

� Fig. 2.4(a) + Fig. 2.4(b) = Fig. 2.4(c)

� There are two component frequencies: f and 3f.

Time-Domain v.s. Frequency-Domain

� Based on Fourier analysis, any signal is made up of components at various frequencies,

� in which each component is a sinusoid wave, at different amplitudes, frequencies, and phases.

� Frequency domain: we represent a signal by recording the amplitudes, frequencies, and phases of its components.

� A signal can be represented either in the time domain, or in the frequency domain.

f [Hz]

A [V]

ϕ

A [V]

t[s]

Frequency-Domain (cont.)

� Spectrum - range of frequencies that a signal contains

� In Fig. 2.4(c), spectrum extends from f to 3f.

� Absolute bandwidth - width of the spectrum of a signal

� In Fig. 2.4(c), it is 3f – f = 2f.

� Effective bandwidth –

� A signal may contain many frequencies.

� But most of the energy may concentrate in a narrow band of frequencies.

� These frequencies are effective bandwidth.

Time-Domain v.s. Frequency-Domain

� Fourier transform

� Inverse Fourier transformf [Hz]

A [V]

ϕ

A [V]

t[s]

ϕ

A [V]

t[s]

f [Hz]

A [V]

Data vs. Signal

� Signals - electric or electromagnetic

representations of data

� Data - entities that convey meanings or

information

� Transmission - communication of data by

the propagation and processing of signals

Approximating Square Wave by Signals

� adding a frequency of 5f to Fig. 2.4(c) � Fig.

2.5(a)

� adding a frequency of 7f to Fig. 2.4(c) � Fig.

2.5(b)

� adding all frequencies of 9f, 11f, 13f, ... � Fig.

2.5(c), a square wave

� This square wave has an infinite number of frequency

components, and thus infinite bandwidth.

Examples of

Analog and Digital Data

� Analog

� Video

� Audio

� Digital

� Text

� Integers

Analog Signaling

Digital Signaling

Reasons for Choosing Data and

Signal Combinations

� Digital data, digital signal

� Equipment for encoding is less expensive than digital-to-analog equipment

� Analog data, digital signal

� Conversion permits use of modern digital transmission and switching equipment

� Digital data, analog signal

� Some transmission media will only propagate analog signals

� Examples include optical fiber and satellite

� Analog data, analog signal

� Analog data easily converted to analog signal

Some Terms about

Channel Capacity

� Data rate - rate at which data can be communicated (bps)

� Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz)

� Noise

� Channel Capacity – the maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions

� Error rate - rate at which errors occur

Signal-to-Noise Ratio

� Ratio of the power in a signal to the power contained in the noise that’s present at a particular point in the transmission

� Typically measured at a receiver

� Signal-to-noise ratio (SNR, or S/N)

� = 10 log10 SNR

� A high SNR means a high-quality signal.

� SNR sets an upper bound on the achievable data rate.

power noise

power signallog10)( 10dB =SNR

Shannon Capacity Formula

� The max. channel capacity:

� note: SNR not in db.

� In practice, only much lower rates are achieved

� Formula assumes white noise (thermal noise)

� Impulse noise is not accounted for

� Attenuation distortion or delay distortion not accounted

for

( )SNR1log2 += BC

Classifications of Transmission

Media

� Transmission Medium

� Physical path between transmitter and receiver

� Guided Media (e.g., wire)

� Waves are guided along a solid medium

� E.g., copper twisted pair, copper coaxial cable, optical fiber

� Unguided Media

� Provides means of transmission but does not guide electromagnetic signals

� Usually referred to as wireless transmission

� E.g., atmosphere, outer space

General Frequency Ranges

� Microwave frequency range

� 1 GHz to 40 GHz

� Directional beams possible

� Suitable for long-distance, point-to-point transmission

� Used for satellite communications

� Radio frequency range

� 30 MHz to 1 GHz

� Suitable for omnidirectional applications

� Infrared frequency range

� Roughly, 3x1011 to 2x1014 Hz

� Useful in local point-to-point multipoint applications within confined areas

Wireless Transmission

Antennas

� Isotropic radiator: equal radiation in all directions

(three dimensional) - only a theoretical reference

antenna

� Real antennas always have directive effects (vertically

and/or horizontally).

� One can use multiple antennas to emulate isotropic

radiator.

zy

x

z

y x ideal

isotropic

radiator

Signal propagation ranges

distance

sender

transmission

detection

interference

� Transmission range

� communication possible

� low error rate

� Detection range

� detection of the signal possible

� no communication possible

� Interference range

� signal may not be detected

� signal adds to the background noise

Signal propagation

� Propagation in free space always like light (straight line)

� Free-space loss: receiving power proportional to 1/d² in

vacuum. (d = distance between sender and receiver)

� Intuition: the signal propagates as a spherical shape. The

surface area is ~ d².

� In real environments the power is between 2 and 5.

� Other effects:

� Fading

� Multi-path propagation

� Movement.

Signal propagation

� Receiving power additionally influenced by

� Shadowing (blocks the signal)

� reflection at large obstacles (with dimension very large compared

to the wave’s wavelength)

� refraction depending on the density of a medium

� scattering at small obstacles (with dimensions in the order of the

wavelength)

� diffraction at edges

reflection scattering diffractionshadowing refraction

� Signal can take many different paths between sender and

receiver due to reflection, scattering, diffraction

� Fast fading: waves traveling along different paths may be

completely out of phase when they reach the antenna

(thereby canceling each other out!)

Multipath propagation

signal at sender

signal at receiver

LOS pulsesmultipathpulses

� Time dispersion: signal is dispersed over time

� � interference with “neighbor” symbols, Inter

Symbol Interference (ISI)

� The signal reaches a receiver directly and phase shifted

� � distorted signal depending on the phases of the

different parts

Multipath propagation

signal at sender

signal at receiver

LOS pulsesmultipathpulses

Effects of mobility

� Channel characteristics change over time and location

� signal paths change

� different delay variations of different signal parts

� different phases of signal parts

� � quick changes in the power received (short term fading)

� Additional changes in

� distance to sender

� obstacles further away

� � slow changes in the average power

received (long term fading)short term fading

long termfading

t

power

Real world example

How to model signal propagation?

� Free space Line-of-sight (LOS) model.

� Too simplified.

� Ray tracing approximation

� Represent wavefronts as simple particles

� Geometry determines received signal from each signal component

� Typically includes reflected rays, can also include scattered and defracted rays.

� Requires site parameters

� Geometry

� Dielectric properties

� Computer packages often used

� Empirical models

Summary

� signal

� analog vs. digital transmissions

� channel capacity

� transmission media

� Signal propagation

� Path loss

� Multi-path propagation